How many three-digit numbers satisfy the property that the middle digit is the average of the first and the last digits?
Answer: The first and last digits must be both odd or both even for their average to be an integer.  There are $5\cdot 5 =25$ odd-odd combinations for the first and last digits.  There are $4\cdot 5=20$ even-even combinations that do not use zero as the first digit. Hence, the total is $\boxed{45}$.